Let z and w be complex numbers such that |z| = |w| = 1, and zw is not equal to -1. Prove that

Question

(z + w)/(zw + 1)
is a real number.

Answer 1

you've been posting this over and over. Did you think of google? Many problems posted here have appeared elsewhere. My first hit on google discusses this problem and one similar to it. Scroll down about halfway and you will find what you need.

http://math.stackexchange.com/questions/427663/prove-if-z-w-1-and-1zw-neq-0-then-zw-over-1zw-is-a-real